The surprise here depends on the probability of survival. If half of people on Earth were Bobs, and other were Alices, then 0.01 chance of survival means that 400 000 Bobs will survive. There is no surprise that some of them survive, neither for Bob nor for Alice.
For example, if you survive until 100 years old, it is not an evidence for quantum immortality.
If, however, survival chance is 1 in 10e12, then even for the whole earth there likely be no Bobs in Copenhagen interpretation. So the existing of Bob is an evidence against it.
For example, if I naturally survive until 150 years old by pure chance, it is evidence for MWI.
Well, really every second that you remain alive is a little bit of bayesian evidence for quantum immortality: the likelihood of death during that second according to quantum immortality is ~0, whereas the likelihood of death if quantum immortality is false is >0. So there is a skewed likelihood ratio in favor of quantum immortality each time you survive one extra second (though of course the bayesian update is very small until you get pretty old, because both hypotheses assign very low probaility to death when young)
If we take the third-person view, there is no update until I am over 120 years old. This approach is more robust as it ignores differences between perspectives and is thus more compatible with Aumann’s theorem: insiders and outsiders will have the same conclusion. Imagine that there are two worlds: 1: 10 billion people live there; 2: 10 trillion people live there. Now we get information that there is a person from one of them who has a survival chance of 1 in a million (but no information on how he was selected). This does not help choose between worlds as such people are present in both worlds. Next, we get information that there is a person, who has a 1 in a trillion chance to survive. Such a person has less than 0.01 chance to exist in the first world, but there are around 8 such people in the second world. (The person, again, is not randomly selected – we just know that she exists.) In that case, the second world is around 100 times more probable to be real. In the Earth case, it would mean that 1000 more variants of Earth are actually existing, which could be best explained by MWI (but alien worlds may also count).
The surprise here depends on the probability of survival. If half of people on Earth were Bobs, and other were Alices, then 0.01 chance of survival means that 400 000 Bobs will survive. There is no surprise that some of them survive, neither for Bob nor for Alice.
For example, if you survive until 100 years old, it is not an evidence for quantum immortality.
If, however, survival chance is 1 in 10e12, then even for the whole earth there likely be no Bobs in Copenhagen interpretation. So the existing of Bob is an evidence against it.
For example, if I naturally survive until 150 years old by pure chance, it is evidence for MWI.
Well, really every second that you remain alive is a little bit of bayesian evidence for quantum immortality: the likelihood of death during that second according to quantum immortality is ~0, whereas the likelihood of death if quantum immortality is false is >0. So there is a skewed likelihood ratio in favor of quantum immortality each time you survive one extra second (though of course the bayesian update is very small until you get pretty old, because both hypotheses assign very low probaility to death when young)
If we take the third-person view, there is no update until I am over 120 years old. This approach is more robust as it ignores differences between perspectives and is thus more compatible with Aumann’s theorem: insiders and outsiders will have the same conclusion.
Imagine that there are two worlds:
1: 10 billion people live there;
2: 10 trillion people live there.
Now we get information that there is a person from one of them who has a survival chance of 1 in a million (but no information on how he was selected). This does not help choose between worlds as such people are present in both worlds.
Next, we get information that there is a person, who has a 1 in a trillion chance to survive. Such a person has less than 0.01 chance to exist in the first world, but there are around 8 such people in the second world. (The person, again, is not randomly selected – we just know that she exists.) In that case, the second world is around 100 times more probable to be real.
In the Earth case, it would mean that 1000 more variants of Earth are actually existing, which could be best explained by MWI (but alien worlds may also count).